The two will play in the same group - along with Joey Sindelar.
Woods and Singh have not shared the same tee time since the first round of the Tour Championship in Houston last November. Neither hides the fact that he is not the other's biggest fan.
'When Vijay and I play, we just play our games. We're trying to win a tournament here,' Woods said. 'It's just the first two days - we're trying to set ourselves up for Sunday. And we have a long way to go.'
While Singh has had more success this year, winning three times to draw to 1.89 points of Woods in the rankings, Woods sounds ready for the showdown.
'Things are starting to come together. I just need to go out there and be patient,' said Woods, who won the Memorial three years in a row from 1999-2001.
Woods hasn't won in his last seven majors after winning seven of the previous 11. But it's not as if he's no longer competitive: he's won two of his last 12 tournaments, three of 18 and six of 27.
There are plenty of other subplots in the 105-player field, which will be serenaded by the screeching cacophony of billions of cicadas, emerging from the ground for the first time in 17 years - they crawl out to mate and lay eggs in tree branches.
The unwelcome visitors will likely interrupt play by flying into players while they are in the midst of a swing or putt, not to mention drowning out the galleries in the leafier parts of the Muirfield Village course.
Another top contender figures to be South Africa's Ernie Els, No. 3 in the world. He won the Sony Open in January and finished second to Mickelson at the Masters.
He's come close to winning at Muirfield Village before - four top-10 finishes including a second to Woods in 2000 - and would like nothing better than to pick up a win to fuel his run for a third U.S. Open title in two weeks at Shinnecock Hills.
'I'm hitting the ball quite nicely so I can't complain,' Els said. 'I just haven't won. I've just got to keep going and working at it and hopefully it'll come by itself.'
Tournament founder and host Jack Nicklaus hinted he is close to saying goodbye to competitive golf. He has backed away from such pronouncements in the past, but he appears committed to devoting more time to his family, fishing and many business interests instead of traipsing the world playing competitive golf.
'This will probably be my last week of playing what I consider tournament golf (this year),' the 64-year-old said. 'It's been eight years since I won a golf tournament. Everything comes to an end somewhere.'
Moments later, however, the winner of 18 major championships spoke as if he was already plotting to take the tour back from players young enough to be his grandsons.
'Do I expect to beat these guys? Absolutely. That's my goal,' he said. 'I'm going to beat as many of them as I can and hopefully beat them all. I don't think that's a realistic goal, but it's something that I would shoot for.'
The field includes nine of the top 12 players in the world rankings. The only ones absent are Phil Mickelson, Mike Weir and the injured Jim Furyk.
Defending champion Kenny Perry and past champs Woods, Fred Couples, Singh, Paul Azinger and Nicklaus are all on hand, along with all but two of the top 13 players on the tour money list.
Nicklaus, who constantly tinkers with the Muirfield layout, added four deep pot bunkers along the right side of the 18th fairway in an effort to penalize long hitters going with a driver on the par-4 hole.
He also completely rebuilt the greens before last year's tournament, then had about 500 trees cut down this year to provide a better air flow and more sunlight to the greens.
'The whole premise to doing that was to bring back some wind into the game,' Woods said. 'If the wind blows, we'll get some openings where the wind will be affecting our second shots.'
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